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Essential details of two techniques for distance measurements between non-identical spin labels are summarized. One technique is based on double electron–electron resonance (DEER) between Gd(iii) ions and nitroxide radicals. The other technique is based on indirect measurements of stochastic dipolar interaction between Ln(iii) ions and organic radicals via the change of longitudinal relaxation of the latter species. Combination of these techniques with double electron–electron resonance in pairs of identical spin labels (nitroxide–nitroxide or Gd(iii)–Gd(iii)) allows to suggest a new experimental strategy for multiple distance measurements in orthogonally-labelled samples. General discussion of advantages and disadvantages of the new strategy for studies of biomacromolecules and their complexes is given along with illustrative experimental examples. In particular, performance of Gd(iii)–nitroxide DEER is compared to other possible combinations of non-identical spin label pairs, while relaxation enhancement in pairs Fe(iii)–organic radical is compared to the case of Dy(iii)–nitroxide pairs.

EPR-based techniques to measure nanometre range distances are nowadays recognized as a valuable tool in studies of structure and conformational changes of biomacromolecules.1–7  A typical approach uses some type of nitroxide-based spin labels, which are selectively attached to specific sites.8–10  The distances between pairs of these spin labels are then measured by some appropriate pulse EPR technique,11–17  most commonly, by the dead-time-free 4-pulse double electron–electron resonance (DEER) experiment.18,19 

As the field of structural and molecular biology proceeds towards more and more demanding objects, such as multi-subunit complexes in solution or in lipid membranes,20–23  development of appropriate EPR methodologies becomes necessary. For instance, while being proved to be robust and sensitive, the nitroxide-based approach does not allow distinguishing between specific labelling sites, because two nitroxide labels are typically very difficult to distinguish spectroscopically. Thus, measurement of the properties of the local environment for a spin label at a particular site requires additional singly-labelled samples. Furthermore, in multiple-subunit systems one is restricted to labelling only two sites per biomolecular complex, otherwise interpretation of the distance distribution gets difficult, as all pairwise distance distributions overlap and cannot be separated from each other. Further difficulties may be caused by the appearance of combination frequencies in the DEER experiment on multiply-labelled biomolecules.24,25 

The number of labelled sites and, thus, the accessible number of distances can be increased by employing non-identical types of spin labels. In this chapter we will discuss an approach of using distinct types of labels for each labelling site in a biomolecule or biomolecular complex under study. We will mainly concentrate on combining nitroxide radicals with chelate complexes of different lanthanide ions,26–29  but other spectroscopic selection options tested so far will be shortly reviewed as well. After providing general introduction in the following part of this section, Sections 2 and 3 will give details of two particular distance measurement approaches for the lanthanide–nitroxide pairs. In Section 4 we will attempt to formulate perspectives of this EPR methodology and discuss its current state of development.

The idea of having two non-identical spin labels that can be distinguished spectroscopically appeared rather early after DEER (sometimes also called PELDOR) and related techniques have attracted considerable attention. It has been demonstrated that 14N/15N labelling of the nitroxide radicals can provide a difference in the nitroxide EPR spectra that is sufficient to distinguish between the two types of labels.30  In another publication, a selective detection of Cu(ii)–nitroxide and nitroxide–nitroxide distance was reported.31  Later, when Gd(iii) chelate complexes were proposed as possible paramagnetic labels for the DEER-based distance measurements,32–34  the performance of the DEER experiment was also studied in Gd(iii)–nitroxide pairs.35–40 

The use of Gd(iii) chelate complexes as the second spin label instead of 15N-labelled nitroxides30  or Cu(ii) complexes31,41–45  offers important advantages. Spectroscopic separation of the signals from nitroxide radicals and Gd(iii) centres relies to a lesser extent on the difference in resonance fields for the two types of paramagnetic species. The main factors that allow spectroscopic separation are the 2–3 orders of magnitude difference in longitudinal relaxation time (at optimum repetition rate for Gd(iii) species nitroxide radicals are nearly completely saturated) and the difference in the transition moments between ‘high-spin’ (S=7/2) Gd(iii) centres and ‘low-spin’ (S=1/2) nitroxide radicals.

formula
Equation 1

For the central, most narrow |−1/2〉↔|+1/2〉 transition of Gd(iii) the ratio of the corresponding transition moment to the one of a nitroxide radical is exactly four, which perfectly suppresses the Gd(iii) signal for the optimal pulse settings of the nitroxide radicals: the Hahn echo detection sequence (π/2–π-echo) tuned for nitroxide radicals would correspond to a 2π–4π-echo sequence on the central Gd(iii) transition, which would ideally produce a zero echo amplitude. For other single-quantum transitions of Gd(iii) the corresponding transition moments of the spin operators are somewhat smaller than the one for the central transition. Still, the overall experimentally observed selection is nearly perfect.35–37  In contrast to this, spectroscopic selection in 14N–15N nitroxide pairs nearly exclusively depends on the (only partial) spectral separation of the signals and is not quantitatively perfect. In Cu(ii)–nitroxide pairs the relaxation time difference can be used as well, but Cu(ii) is an S=1/2 system, and thus the transition-moment-based selection is not available in this case. The Cu(iii) EPR spectrum at Q-band and higher detection frequencies is also broader than that of the |−1/2〉↔|+1/2〉 transition of Gd(iii) centres. Therefore, more Gd(iii) species can be excited by a microwave pulse of a given bandwidth, thus providing a sensitivity advantage. Cu(ii) centres also typically have a strong spectroscopic separation of different orientations of the complex with respect to the applied static magnetic field. In contrast, Gd(iii) chelates seem to have no orientation selectivity at any spectral position. This significantly simplifies applications where distance information is required. The orientation information can still be assessed, if necessary, via selective excitation of nitroxide labels.38 

A further type of spin labels that can be sufficiently well separated spectroscopically both from the nitroxide radicals and the Gd(iii) centres are the trityl radicals that were recently reconsidered for pulse EPR distance measurements.46–48  In this case, the spectroscopic separation of the trityl and nitroxide radicals is mainly due to the difference in resonance fields.47  Still, due to the very narrow spectrum of trityl such a separation can be sufficiently good. A disadvantage of trityl radical is its large size that might limit the range of biochemical applications of such a spin label.

Another line of spectroscopic selection options appears if the second spin label is essentially invisible in the pulse EPR measurements. This is the case if chelate complexes of any trivalent paramagnetic lanthanide ions [except Gd(iii)] are used as spin labels. Those lanthanide ions relax fast enough to be non-detectable in any pulse EPR experiment at least down to ∼10 K. Such a spin label would not lead to any spectral crowding problem, but its dipole–dipole interaction with nitroxide radicals can still be measured via the relaxation enhancement (RE) effect.

The relaxation enhancement-based distance measurements were initially proposed for continuous wave (CW) EPR.49  The CW EPR-based techniques can be utilized at ambient temperature, which is closer to the physiological conditions. (In contrast to this, pulse EPR experiments are almost exclusively done at low temperatures, with the solvent in a frozen glassy state.) Interestingly, applications of lanthanide ions as relaxing agents were suggested in the early research. Later, however, the CW EPR approaches based on Ni or Cr complexes became more popular.50–53  These techniques are mostly considered to be qualitative, in particular due to the interference between relaxation enhancement and molecular motion.

In a series of papers of S. S. Eaton, G. R. Eaton and co-workers, distances from organic radicals to a transition metal centre (mainly Fe(iii)) were measured by pulse EPR relaxation techniques. These reports and contributions from other groups up to the year 2000 were reviewed,54  but to date did not lead to a broad range of applications, partially due to a quick spread of DEER-based approaches at about the same time. It is also important to mention that initially RE-based distance measurements were mainly concentrating on protein molecules, naturally containing transition metal centres (e.g., methemoglobin), while the DEER technique was from the beginning combined with site-directed spin labelling (SDSL) which allowed for studying a much broader range of systems. Still, several interesting papers on RE were since published by different groups, in particular, clarifying some important theoretical points, data analysis procedures, and testing SDSL approaches and new label types.55–63  While static dipolar interaction exploited in the DEER technique allows for a more straightforward distance calculation, the RE technique requires certain assumptions on the characteristic correlation time for stochastic fluctuations of the fast relaxing spin label. Moreover, the presence of further paramagnetic centres in the sample may cause interference with the RE effect in a given spin-label pair.60  Thus, further development of the RE-based distance measurement technique required calibration against well-established DEER measurements. In this case use of lanthanide tags provides a very convenient option of exchanging fast relaxing ions by slowly relaxing Gd(iii) and thus calibrating RE distance measurements against DEER in geometrically nearly identical Gd(iii)–nitroxide pairs.61,62  A detailed analysis of this technique and discussion of its precision and possible application area will be given in Section 3.

To summarize, combination of lanthanide chelate complexes and nitroxide radicals allows for a series of different types of distance measurements presented schematically in Fig. 1 (along with schematic representation of two possible experimental situations, where such a scheme would be useful). Inclusion of further labels, such as trityl, into this scheme would be rather straightforward. The scheme consists of distance measurements between identical spin labels (DEER in nitroxide–nitroxide and Gd(iii)–Gd(iii) spin pairs) and between non-identical spin labels (RE experiment in the nitroxide–Dy(iii) pairs or DEER in the nitroxide–Gd(iii) pairs). The newest developments for the DEER technique on pairs of identical spin labels were recently reviewed.7,64  In the following two sections we will overview specific details of the distance measurements between non-identical labels. After that, in the final section, a general discussion of the current state and future perspectives of this new experimental strategy will be given.

Figure 1.1

Schematic representation of the orthogonal labelling strategy for combination of nitroxide radicals and lanthanide complexes. (A) Types of distance measurements reported to date. Note the directional arrows for the non-identical label pairs. (B) A schematic representation of a three-subunit macromolecular complex, which could be a target of orthogonal labelling strategy. (C) A schematic representation of a weak complex between a larger biomolecule and a smaller cofactor (or substrate, or inhibitor) molecule. In case of weak complex, large number of free molecules needs to be present in the sample which would not allow performing distance measurements with conventional labelling strategies, based on identical spin labels at both sites. In contrast, orthogonal labelling would be appropriate in such cases.

Figure 1.1

Schematic representation of the orthogonal labelling strategy for combination of nitroxide radicals and lanthanide complexes. (A) Types of distance measurements reported to date. Note the directional arrows for the non-identical label pairs. (B) A schematic representation of a three-subunit macromolecular complex, which could be a target of orthogonal labelling strategy. (C) A schematic representation of a weak complex between a larger biomolecule and a smaller cofactor (or substrate, or inhibitor) molecule. In case of weak complex, large number of free molecules needs to be present in the sample which would not allow performing distance measurements with conventional labelling strategies, based on identical spin labels at both sites. In contrast, orthogonal labelling would be appropriate in such cases.

Close modal

The echo-detected EPR spectra simulated for nitroxide radicals and Gd(iii)–DOTA complexes at the three most common detection bands (X, Q and W band, i.e., ∼9.5, ∼34 and ∼95 GHz detection frequency) are presented in Fig. 2. The spectrum of nitroxide radicals mainly consists of three anisotropically broadened sub-spectra corresponding to the three spin states of a paramagnetic 14N nucleus (mI=+1, 0, −1). There is interplay between g- and hyperfine anisotropy for each of the three sub-spectra. As a result, at X band the central one (mI=0) has least cumulative anisotropy and the maximum intensity in the nitroxide spectrum is close to its centre. At Q band the low-field sub-spectrum (mI=+1) gets least broadened as the g- and hyperfine anisotropies nearly compensate each other in that case. At W and higher bands the g-anisotropy dominates the spectrum, all three sub-spectra strongly overlap (except of the gz region) and the maximum of the spectrum is again in the centre close to the gy position.

Figure 1.2

Numeric simulations of the EPR spectra of nitroxide radicals ((A)–(C)) and Gd(iii) complexes ((D)–(F)). For both species the spectra were computed for the X-band detection frequency (9.5 GHz, (A) and (D)) as well as for Q band (35 GHz, (B) and (E)) and W band (95 GHz, (C) and (F)). Spectra were simulated with EasySpin software (www.easyspin.org). Spectroscopic parameters for nitroxide radicals: g-tensor eigenvalues – [2.0085 2.0061 2.0022], 14N hyperfine tensor eigenvalues – [13 13 100] MHz, FWHM – [0.3 0.3] mT (mixed Lorentzian/Gaussian line shape). For nitroxide radicals subspectra corresponding to the 14N spin projection of +1 (left subspectrum), 0 (middle subspectrum), and −1 (right subspectrum) are plotted as dashed lines. Spectroscopic parameters for Gd(iii) centres: isotropic g-value of 1.991; D-values normally distributed with 〈D〉=1500 MHz and σ(D)=〈D〉/5; D/E values distributed, according to P(x)=x/3−2x2/9 (see ref. 29 and 65).

Figure 1.2

Numeric simulations of the EPR spectra of nitroxide radicals ((A)–(C)) and Gd(iii) complexes ((D)–(F)). For both species the spectra were computed for the X-band detection frequency (9.5 GHz, (A) and (D)) as well as for Q band (35 GHz, (B) and (E)) and W band (95 GHz, (C) and (F)). Spectra were simulated with EasySpin software (www.easyspin.org). Spectroscopic parameters for nitroxide radicals: g-tensor eigenvalues – [2.0085 2.0061 2.0022], 14N hyperfine tensor eigenvalues – [13 13 100] MHz, FWHM – [0.3 0.3] mT (mixed Lorentzian/Gaussian line shape). For nitroxide radicals subspectra corresponding to the 14N spin projection of +1 (left subspectrum), 0 (middle subspectrum), and −1 (right subspectrum) are plotted as dashed lines. Spectroscopic parameters for Gd(iii) centres: isotropic g-value of 1.991; D-values normally distributed with 〈D〉=1500 MHz and σ(D)=〈D〉/5; D/E values distributed, according to P(x)=x/3−2x2/9 (see ref. 29 and 65).

Close modal

For so called orientation selection measurements (see Section 2.2) it is important how well different orientations of g- and hyperfine tensors are separated in the EPR spectrum. While different hyperfine sub-spectra overlap stronger in the order X<Q<W band, the spectral positions of different principal components of g- and hyperfine tensors move closer to each other in this order, and the spectral resolution increases with the increase of the detection frequency. Therefore, among these three bands, despite stronger sub-spectra overlap, the measurements at W band offer best spectral selectivity for nitroxide orientations.

The EPR spectrum of the Gd(iii) centre (S=7/2) consists of 7 single quantum transitions. The lowest energy multiplet of Gd(iii) is 8S7/2 which has nearly zero angular momentum and therefore the smallest strength of the zero-field splitting (ZFS) term in the spin Hamiltonian among all Ln(iii) ions. This results in an orders of magnitude slower relaxation of Gd(iii) and in a relatively weak ZFS that in most cases allows to describe this ion in a high-field approximation with ZFS as a perturbation correction to the electron Zeeman interaction (this is true at Q and higher bands). As Gd(iii) is a Kramers type ion, it has a |−1/2〉↔|+1/2〉 transition that is only weakly (as a second order perturbation) broadened due to the ZFS term in the spin Hamiltonian. Thus, a typical spectrum of Gd(iii) complex detected at Q-band or higher frequencies has a sharp line in the centre due to the |−1/2〉↔|+1/2〉 transition, on top of a significantly broader bell-like shaped background that arises from the overlap of all other transitions (see Fig. 2). Notably, despite the presence of multiple canonical orientations and turning points in the angular dependencies of the resonance fields for different transitions in such a high-spin centre, no pronounced kinks or peaks are present in the EPR spectra of different Gd(iii) chelate complexes measured in frozen solutions.65  This clearly indicates a broad distribution of ZFS parameters for such samples, resulting in virtually complete absence of preferred Gd(iii) complex orientations at any detection position in its EPR spectrum. It has been suggested, that such a distribution can be present due to a dynamic nature of the corresponding chelate complexes. The typically used Gd(iii) chelators, such as DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid) or DTPA (diethylene triamine pentaacetic acid) have “arms” with carboxylic groups at the end, which can rearrange to a certain extent around the lanthanide ion.29,65  Often there is a space for one or more additional water ligands.26,29  This leads to the presence of complexes with no, one and, eventually, more water ligands, thus creating an additional contribution to the distribution of ZFS parameters.

The ZFS term in the spin Hamiltonian of Gd(iii) is usually simplified to only quadratic terms in the spin operators.29  In that case a general form of the ZFS term, in its own eigenbasis is

formula
Equation 2

For a perfect high-field case, where electron Zeeman interaction dominates ZFS and all other terms in the spin Hamiltonian, the only secular term in the dipolar interaction is given by

formula
Equation 3

The value relevant in DEER experiment is not the dipolar interaction itself, but rather the change of dipolar interaction between two states, which is in high-field approximation identical for all single-quantum transitions of Gd(iii) and given by

formula
Equation 4

The positive or negative sign refers to the state of nitroxide spin |+1/2〉 or |−1/2〉 and to the sign of the difference in magnetic quantum numbers mS and mS′ of Gd(iii) during the transition mSmS′.

The ZFS of Gd(iii)-centres is, however, not negligibly small, as compared to the electron Zeeman interaction, and especially at low detection frequencies and strong ZFS, can even be of almost the same magnitude. This leads to corrections for the eigenstates of the complete spin Hamiltonian. As a result, the secular part of dipolar interaction is also modified and the dipolar frequency between two states from eqn (4) can be generally expressed as

formula
Equation 5

Here and in eqn (3) and (4)θ is a polar angle between the static magnetic field and the inter-spin vector. The azimuthal angle φ is determined as an angle between the vector Δm and the component of the inter-spin vector, perpendicular to the static magnetic field. The values Δm and Δm are transition specific, depend on the strength of ZFS (D and E values) and on the orientation of the ZFS tensor with respect to the static magnetic field.36  In the limiting case of very strong magnetic field, for all single quantum transitions of Gd(iii) the relations Δm → 0 and Δm → 1 hold. An example of simulated Δm and Δm distributions for D=1500 MHz and detection frequency of 9.5 GHz (X band) are shown in Fig. 3. On the same figure, a dipolar frequency pattern is shown, which is simulated for the same case for an infinitely narrow distance distribution with a Gd(iii)–nitroxide distance of 3 nm. One can see that the dipolar frequency pattern is broadened compared to the classical high-field Pake pattern. If distance analysis is performed according to the high-field approximation, without correction for ZFS,36  the obtained distance distribution would be somewhat broadened as shown in Fig. 4. Note that the positions of the “horns” in the dipolar frequency pattern are only weakly affected by this distortion (Fig. 3(B)). This is a consequence of the fortunate angular dependence of the distorting term in (see eqn (5)), which is equal to zero at both canonical orientations θ=0° and θ=90°. As a result, only a very small shift of the mean distance is induced by such approximate distance analysis (〈〉=2.96 nm, instead of 3 nm, Fig. 4(B). As nearly all frequently used Gd(iii) chelate complexes have D-values of ∼2 GHz or less, such a distortion of distance distribution is mainly important for X-band experiments. At Q band, the artificial broadening of distance distribution can only be seen in very special cases, when particularly narrow distance distributions of a width of 1–2 Å are present, while at W and higher bands this effect is negligibly small.

Figure 1.3

Distributions of parameters Δm|| (A) and Δm (B) and the overall dipolar frequency pattern (C) computed for the Gd(iii) complexes with D=1500 MHz and Gd(iii)–nitroxide distance of 3 nm at X band. See eqn (2)(5). Data from ref. 36.

Figure 1.3

Distributions of parameters Δm|| (A) and Δm (B) and the overall dipolar frequency pattern (C) computed for the Gd(iii) complexes with D=1500 MHz and Gd(iii)–nitroxide distance of 3 nm at X band. See eqn (2)(5). Data from ref. 36.

Close modal
Figure 1.4

Simulations of the distance distribution broadening for the Gd(iii) complexes with D=1500 MHz and a single Gd(iii)–nitroxide distance of 3 nm at X band: (A) simulated DEER trace (solid line) and its fit with DeerAnalysis software (dashed line); (B) resulting distance distribution (dotted vertical line indicates the single distance input). Data from ref. 36.

Figure 1.4

Simulations of the distance distribution broadening for the Gd(iii) complexes with D=1500 MHz and a single Gd(iii)–nitroxide distance of 3 nm at X band: (A) simulated DEER trace (solid line) and its fit with DeerAnalysis software (dashed line); (B) resulting distance distribution (dotted vertical line indicates the single distance input). Data from ref. 36.

Close modal

The pulse sequence of the 4-pulse DEER experiment (Fig. 5) consists of a refocused echo sequence for the observer frequency and of an inversion pulse acting on the pumped frequency. The amplitude of the detected refocused spin echo is determined by the amplitude of the primary Hahn echo (VHahn) and the decay of the transverse magnetization during the refocusing block. In the DEER experiment only a certain fraction of the echo amplitude is modulated with the dipolar frequency. This fraction λ, often called modulation depth, determines the actual amplitude of dipolar oscillations. The overall signal-to-noise ratio (SNR) in the DEER experiment is determined by this amplitude and by the rate with which the experiment can be repeated, the latter value being inversely proportional to the longitudinal relaxation time T1. Eqn (6) summarizes all these effects in mathematical form, with T2 being the transverse relaxation time, and τ2 being the second delay time in the DEER pulse sequence:

formula
Equation 6
Figure 1.5

Pulse scheme and frequency settings for the DEER in Gd(iii)–nitroxide spin pairs. (A) Q-band spectra of nitroxide radicals and Gd(iii) centres with positions of pump and observer frequencies indicated by arrows. (B) Scheme of pulses for each of the two frequencies.

Figure 1.5

Pulse scheme and frequency settings for the DEER in Gd(iii)–nitroxide spin pairs. (A) Q-band spectra of nitroxide radicals and Gd(iii) centres with positions of pump and observer frequencies indicated by arrows. (B) Scheme of pulses for each of the two frequencies.

Close modal

For a fixed value of the first time delay τ1, the amplitude of the Hahn echo is determined by the thermal polarization and the cumulative excitation bandwidth of the detection pulses. While in a two-level system (S=1/2) the thermal polarization continuously grows with decreasing measurement temperature, in a multilevel system, as it is the case for Gd(iii) centres (S=7/2, eight levels), the polarization of a pair of levels, of which none corresponds to the lowest energy in the multiplet, would attain its maximum at a certain non-zero temperature. Below that temperature the polarization decreases as both levels get depopulated. For instance, for the |−1/2〉↔|+1/2〉 transition of Gd(iii) the optimum polarization is reached at ∼3 K in the magnetic field of about 1.25 Tesla (Q band, detection frequency ∼34 GHz) and at ∼10 K in the magnetic field of about 3.4 Tesla (W band, 95 GHz).64  This transition dominates in the echo signal at W and higher bands provided that the detection frequency is set to the maximum of the Gd(iii) EPR spectrum and that transverse relaxation of that transition is slower or the same as the relaxation of other Gd(iii) transitions. At Q band this transition can be significantly broader, especially for chelate complexes with large ZFS, and it might not fully dominate the detected signal. The Gd(iii)–nitroxide DEER experiment can also be performed at X band (∼9.5 GHz, 0.34 Tesla).35,36,39,40  In that case all transitions of Gd(iii) centres have similar widths and the determination of the optimum polarization temperature would depend on the ZFS parameters of a particular complex, but in most cases the optimum would be placed below 3 K which is difficult to reach with commonly used He-flow cryostats. Regarding technical issues, such as spectrometer phase stability (for waveguide-based resonators, where moisture condensation could be an issue) and Helium consumption, slightly higher measurement temperatures of about 5–10 K seem to be more convenient despite some loss in polarization. For the few Gd(iii) complexes tested so far, transverse relaxation gets slower at least down to 5–10 K,35,40  at the same time longitudinal relaxation gets slower as well, which reduces the repetition rate and partially diminishes the effect of higher Hahn echo intensities at lower temperatures.35  Sample deuteration has a strong effect on the transverse relaxation of the Gd(iii) complexes and allows for either a significant increase in the SNR or for a measurement of longer DEER traces and, accordingly, longer spin–spin distances. To date the maximum length of a Gd(iii)–Gd(iii) or Gd(iii)–nitroxide DEER trace that has been reported is 12 μs, which allows to access distances up to ∼8 nm.38,66  At X band, due to the echo modulation upon the interaction with deuterium nuclei, the DEER sensitivity enhancement for deuterated samples is less pronounced.35  Still, longer distances can be assessed, as compared to protonated samples.

The increase of SNR upon increasing the excitation bandwidth of detection pulses has two origins. First, the integral echo intensity increases as more spins are excited. Second, the width of the echo narrows down in the time domain, thus, the peak signal amplitude further increases and the intensity of noise gets down as the integration window is reduced. In the DEER experiment an additional gain is the increased modulation depth for a pump pulse with larger excitation bandwidth. Therefore, high-power setups are quite advantageous as it was demonstrated at Q band for nitroxide–nitroxide DEER67  and as it is certainly the case also for DEER measurements in Gd(iii)–nitroxide pairs.35,36 

The transverse and longitudinal relaxation of pumped spins does not play a significant role in DEER sensitivity, unless the longitudinal relaxation of pumped spins gets comparable or faster than the transverse relaxation of detected spins. In the latter case some part of dipolar oscillations could be damped due to spontaneous flips of the pumped spin during the evolution period.

The DEER modulation depth is proportional to the fraction of species, whose magnetization is inverted by the pump pulse. This can be increased by a larger excitation bandwidth of the pump pulse and by the selection of the pump frequency at the optimum position in the corresponding EPR spectrum. Thus, for optimal sensitivity, the Gd(iii)–nitroxide DEER is usually set up with the detection frequency at the maximum of the Gd(iii) spectrum and pump frequency at the maximum of the nitroxide spectrum. This setting corresponds to a pump-detection frequency difference of ∼85 MHz at X band, ∼300 MHz at Q band and ∼700 MHz at W band. At X band the required frequency splitting is achievable with dielectric or split-ring commercial resonators, at Q band resonators with a sufficiently broad single mode are available.68 

As the nitroxide species require higher microwave power for the same length and turning angle of a pulse, it is more convenient to set the pump frequency close to the centre of the resonator mode, while setting up the detection pulses for Gd(iii) species on the shoulder of the mode, although this slightly diminishes detection sensitivity. Such a setup might be further improved by using a bimodal resonator, as this improves both the bandwidths of detection pulses and the coupling of the echo signal to the microwave line. At W band, to reach the optimum frequency separation, either a bimodal resonator69  or a resonator-free approach70  can be exploited. In the latter approach, the loss in detection sensitivity is overcompensated by an increase in sample volume. As the Gd(iii)–nitroxide DEER has to be set up at 5–10 K, where nitroxide radicals typically have very slow longitudinal relaxation, it is convenient to first make a pulse setup on Gd(iii) centres at the maximum of Gd(iii) EPR spectrum and then to increase the microwave power by 12 dB with a precise attenuator. Such a power increase changes the nominal turning angle by a factor of four, which to a good approximation corresponds to the proper pulse settings of nitroxide radicals. This helps speeding up the tuning process.

It is known that, whenever excitation bands of the detection and pump pulses are close, a reduction of echo amplitude due to a Bloch–Siegert mechanism takes place.71,72  This effect is particularly important for Gd(iii)–nitroxide pairs: as the pump pulse is set up to flip low-spin nitroxide species, it has a higher turning angle (∼3–4π, instead of π) for the Gd(iii) species. Therefore, for the same frequency offset the effect of echo reduction is stronger for Gd(iii)–nitroxide pairs37  as compared to pairs of identical spin-centres, like nitroxide–nitroxide or Gd(iii)–Gd(iii).

In addition to the Bloch–Siegert mechanism that is general for all paramagnetic species, another mechanism, specific for high-spin centres, plays an important role in DEER echo reduction on Gd(iii) species.36  If the frequency of the pump pulse is resonant with a transition that has a level in common with the transition already excited by the detection pulse sequence, then single-quantum coherence created by the detection pulses is partially or fully transferred to non-detectable double-quantum coherence.

The contribution of this effect depends on the strength of ZFS for a particular type of Gd(iii) centres, because, depending on ZFS, a larger or smaller fraction of each transition is excited by the pump pulse and also because the strength of ZFS changes angular dependencies for the differences of resonance frequencies for pairs of Gd(iii) transitions with a level in common. For instance, at X and Q band the refocused echo amplitude gets reduced down to 30–40% of its initial amplitude for Gd(iii)–DTPA complexes, while it is reduced down to 1–10% for Gd(iii)–DOTA complexes, which have more symmetric structure and, thus, weaker ZFS.36,39,40 

The reduction of the refocused echo leads to a loss of sensitivity for Gd(iii)–nitroxide DEER. Still, available Q-band data suggest approximately the same concentration sensitivity for Gd(iii)–nitroxide and nitroxide–nitroxide DEER. At W and higher bands the optimal pump-detection frequency offset is already large enough to ensure practically no echo reduction by either of the two mechanisms.

At Q band it was shown that for a moderate decrease of the bandwidth or turning angle of the pump pulse the recovery of the DEER echo amplitude is stronger than the loss in modulation depth.40  As a result, optimal SNR in Gd(iii)–nitroxide DEER is achieved at a nominal flip angle for the pump pulse between 2π/3 and π/2 rather than π. A stronger sensitivity improvement is characteristic for complexes with weak ZFS, while the effect is not so dramatic for complexes with relatively strong ZFS. For instance for Gd(iii)–DOTA (D ≈ 500 MHz) the SNR improves by about a factor of 2.5–3.0, which results in almost an order of magnitude reduction of the measurement time. For a Gd(iii)–DTPA complex (D ≈ 1500 MHz) only about 40–50% of SNR improvement was observed.

No dependence of the shape of the DEER time trace was detected for different flip angles of the pump pulse, and no detectable change of the magnitude of echo reduction was observed upon changing the evolution time in Gd(iii)–nitroxide DEER experiment.36,40  This allows one to conclude that while influencing the SNR, the echo reduction effect does not lead to significant distortions in the obtained distance distributions.

If the orientations of eigenframes of paramagnetic centres correlate with the orientation of the inter-spin vector, the mutual orientation of the two spin labels or their orientations with respect to the labelled macromolecule can be obtained from DEER in addition to the inter-spin distance information.6,17,73,74  Experimentally this is done by measuring and analysing series of DEER traces with narrower excitation bandwidth of the microwave pulses for different positions of pump and detection frequency. In case of a pair of nitroxide labels, at high detection frequencies, where x- and y-components are distinguishable, the fit of such a series of traces includes determination of five angles: orientation of the inter-spin vector with respect to the eigenframe of one of the nitroxide labels and the three Euler angles, determining the orientation of the second label's eigenframe with respect to the first one. For a Gd(iii)–nitroxide case, the Gd(iii) label does not reveal any orientational selectivity, thus, only orientation of one nitroxide label with respect to the inter-spin vector is to be determined.38  This reduces the number of angles to be fitted to only two. In the majority of cases one has to consider a distribution for each angle, which increases the number of fit parameters by at least a factor of two (for a fixed shape of each distribution). In such a multi-dimensional parameter fit situation, the reduced number of fit parameters is a strong argument for using Gd(iii)–nitroxide pairs instead of nitroxide–nitroxide pairs. This can also allow for using non-selective detection pulses with broader bandwidth and, thus, better sensitivity. The latter can be further aided by the narrowing of the central transition of Gd(iii) centres at high fields/high detection frequencies, where better angular resolution for nitroxide radicals is also achieved.

To perform Gd(iii)–nitroxide DEER or Ln(iii)–nitroxide RE on a biological sample it is necessary to introduce two different types of labels into the same biomacromolecule or biomacromolecular complex. If only two sites are to be labelled, it is, in principle, possible to statistically label both sites with both types of labels.37,38  However, such an approach would lead to a 50% or higher loss of sensitivity (50% loss, assuming equal labelling efficiency for both types of labels). In addition, statistical labelling leads to a loss of label-site assignment, as both label types would be present at both sites. Still, at high detection frequencies Gd(iii)–nitroxide DEER might be more advantageous than the ‘conventional’ nitroxide–nitroxide DEER due to, for instance, less complicated orientation selection. Note however that statistical labelling complicates the situation by introducing two nitroxide molecular frames instead of only one. For any system with more than two labelling sites statistical labelling with non-identical labels has no advantage compared to labelling with only one type of labels, while site specific labelling with non-identical labels allows for extracting more information from a single sample. Such site-specific labelling basically implies a possibility to perform chemically selective label attachments at two different sites of a biomolecule. For proteins this is possible with use of an unnatural amino-acid in addition to a more conventional SH-specific attachment of a paramagnetic label to a cysteine.40,75  The reaction of an acetyl group in the unnatural amino acid with a hydroxylamine pendant of a nitroxide derivative, used in the cited work, requires relatively harsh conditions (pH 4), which would not be appropriate for every protein, but could be tolerated by, e.g., T4-lysozyme.75  The attachment of a Gd(iii) chelate via reaction of a maleimido group with the SH moiety of cysteine, in turn was rather straightforward.40 

Importantly, a tendency of Gd(iii) chelates to non-specifically bind to the surface of protein was observed. However, the admixture of glycerol to the protein solution, which is required prior to the sample freezing, could remove the non-specifically bound Gd(iii) chelates from the protein surface.40  While correct and relatively narrow distance distributions were observed in Gd(iii)–nitroxide DEER, the modulation depth was strongly reduced due to the contamination from isolated Gd(iii) species detached from the protein. This issue could be resolved by using a buffer with 10% glycerol admixture during sample preparation. Some other lanthanide binding chemistries were tested in connection with paramagnetic NMR applications.76,77 

It can be also possible to use identical chemistry to attach two different types of spin labels, provided one of the labelling sites can be temporarily protected during the attachment of the first type of spin label. An example of such protection is given by the case of lactose permease of E. coli.78 

Orthogonal labelling of macromolecular complexes is possible with the same attachment chemistry for all types of labels, if only one type of label is attached to each subunit, and if different subunits of the complex can be labelled prior to complex formation. If this is not possible, approaches similar to labelling of monomeric protein molecules need to be exploited. In cases when one spin label is placed on a smaller peptide or an organic cofactor or inhibitor, such a molecule could be chemically modified to add a paramagnetic moiety, as it has been done on synthetic WALP23 polypeptides, where a modified Ln(iii)–DOTA–lysine residue was added at the N-terminus during peptide synthesis.39,60,61 

In general, while several useful options for orthogonal labelling are already available, this is clearly a playground for further inventions. Especially the range of techniques to orthogonally label monomeric macromolecules needs to be enhanced.

Distance measurements by relaxation enhancement are much less popular in EPR as compared to NMR spectroscopy, where constraints based on the nuclear Overhauser effect79,80  or paramagnetic relaxation enhancement81,82  often play an important role in macromolecular structure determination. Such an underrepresentation of RE-based distance measurements in EPR is only partially connected to the fast and broad spread of the DEER technique. The RE approach has its internal difficulties that have to be overcome in order to secure broad and robust applicability of the method. We shall see in the following that while the RE approach is useful to derive qualitative conclusions, in its current state it has to be applied with care for measurement of precise distances. The perspectives for resolving this precision issue will be briefly discussed in the last section.

The extraction of spin–spin distance from a relaxation measurement is based on the effect of the change of the relaxation rate for a slowly relaxing paramagnetic species (typically, organic radicals) induced by a rapidly fluctuating stochastic magnetic dipolar interaction ̂Hd with a fast relaxing paramagnetic species (typically, transition metal or lanthanide centres).49 

The simplest close-form description of the relaxation enhancement is achieved if the second order perturbation theory of Bloch–Wangsness–Redfield (BWR)83,84  is applicable. The starting equation for the BWR description is the second order perturbation formula for the evolution of the spin density matrix:85,86 

formula
Equation 7

The value of ̂ρ(t) is assumed to change slowly as compared to ̂Hd(t) and can thus be approximated as a constant during the integration process. Furthermore, the upper integration limit T can be shifted towards +∞, under an assumption that during the time, comparable to the correlation time τC of stochastic dipolar interaction, the change in the density matrix is small. One, thus, needs a condition ‖̂Hd‖·τC≪1 to be fulfilled. For a typical strength of dipolar interaction (0.1–50 MHz) and typical relaxation times of, e.g., Dy(iii) centres of ∼10−11 s, this condition is safely valid.

The usual way of solving eqn (7) requires its transformation into the interaction representation (Dirac picture) that is often called “rotating frame” for a particular case, when static part of the spin Hamiltonian is restricted to the electron Zeeman interaction. In the Dirac picture only the stochastic dipolar interaction is left in the spin Hamiltonian, its matrix elements get additional oscillatory factors due to the static Hamiltonian transitions. The integral on each matrix element of the double commutator in eqn (7) thus evolves into the Fourier transform J(ωi) of the correlation function for the corresponding stochastic process. This Fourier transform is often called spectral density of the stochastic process and it is to be taken at a frequency ωi of a particular transition of the static Hamiltonian operator, driven by a single transition operator ̂Ki:

formula
Equation 8

In eqn (8) one has to sum over all operators ̂Ki that together compose the magnetic dipole–dipole interaction. For Ln(iii) ions (with exception of Gd(iii)) the splitting at zero field is much stronger than the electron Zeeman interaction and at the temperatures of interest (10–100 K) mainly the lowest level (non-Kramers case) or pair of levels (Kramers case) in the ground J-multiplet is populated. We will mainly discuss the case of Kramers-type Dy(iii) ion for which the lowest lying |±15/2〉 doublet is separated by about one or few THz from the closest |±13/2〉 doublet. Based on this consideration, the existing models for Dy(iii)-induced relaxation enhancement assume that it is mainly driven by the transitions within the |±15/2〉 doublet.59  The Dy(iii) centre is thus described as an effective spin 1/2 with a strongly anisotropic g-tensor. Within the |±15/2〉 doublet, in turn, the high-temperature approximation is valid (the splitting between these levels is determined by the electron Zeeman interaction, which is weak compared to the thermal energy kBT).

It is sometimes convenient to write the dipolar Hamiltonian as a sum of simpler spin operators, according to so called “dipolar alphabet”:

̂Hdd=ωdd(̂A+̂B+̂C+̂D+̂E+̂F)
Equation 9

where

formula
Equation 10

For a pair of S=1/2 species each of these operators drives a particular transition of the two-spin system. Inserting the spin operators from eqn (10) into eqn (8) leads to the relaxation enhancement equations in the form:49 

formula
Equation 11
formula
Equation 12

where the RE values Δk1,2 are defined as a difference of inverted relaxation times in the presence (1/T1,1/T2) and in the absence (1/T1,0,1/T2,0) of the fast relaxing species:

formula
Equation 13

and the spectral density function has the form

formula
Equation 14

The subscript ‘f’ denotes fast relaxing species parameters, while the subscript ‘s’ stands for slowly relaxing species’ parameters. The subscript ‘0’ indicates measurements in the absence of fast relaxing species. One can see that, as RE is a second order perturbation effect, its magnitude is proportional to a square of dipole–dipole interaction and thus scales with inter-spin distance as r−6.

One can further see from eqn (11) and (12) that the distance extraction is possible both from longitudinal and from transverse relaxation data. Nevertheless, distance measurements based on longitudinal relaxation seem to be more advantageous for two reasons. First, longitudinal relaxation of nitroxide radicals (and most other organic radicals), which can be used as slowly relaxing species in such a distance measurement scheme, is typically a few orders of magnitude slower than their transverse relaxation, thus allowing for detection of much smaller changes in relaxation, and, accordingly, longer distances. Second, the transverse relaxation of paramagnetic species is noticeably stronger affected by the surrounding magnetic nuclei than the longitudinal relaxation. For instance, by deuterating the solvent one can change the transverse relaxation time of nitroxide radicals by about one order of magnitude, while the longitudinal relaxation is nearly unaffected by such a solvent modification.87,88  Such an unwanted interference with other spins may cause difficulties in distance determination.

For proper distance determination with RE techniques it is important that the total change of the relaxation rate for slowly relaxing spin is caused exclusively by the stochastic dipolar interaction with the second spin. Thus, for the RE technique the presence of a third paramagnetic species in the vicinity of the spin pair is a complication. As it is schematically shown in the Fig. 6, each of the three paramagnetic species would in principle affect relaxation properties of the other two. This effect was demonstrated on WALP23 polypeptides labelled with nitroxide radicals and Ln(iii) chelates in a model 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membrane with some residual amounts of dissolved oxygen.60  The relaxation rate for nitroxide radicals in the presence of both Dy(iii) chelates and small amounts of oxygen was compared to the case when only oxygen molecules were present close to nitroxide radicals. The change of nitroxide relaxation in this case contained a contribution due to the direct stochastic dipolar interaction with Dy(iii) as well as an indirect contribution from the changed relaxation enhancement of oxygen, as oxygen's own relaxation properties are also modified in the presence of Dy(iii). The observed effect accounted for about 20% change of the total RE value, but it would be much stronger in a non-degassed lipid membrane, saturated with dissolved oxygen.

Figure 1.6

Multiple pathway RE in nitroxide–Dy(iii)–O2 three spin system. The RE induced by Dy(iii) on nitroxide species increases in the presence of O2 (upper curve in the plot and upper scheme) due to the indirect RE mechanism via dioxygen. In the absence of O2 (lower curve in the plot and lower scheme) real RE value is measured. Data from ref. 60.

Figure 1.6

Multiple pathway RE in nitroxide–Dy(iii)–O2 three spin system. The RE induced by Dy(iii) on nitroxide species increases in the presence of O2 (upper curve in the plot and upper scheme) due to the indirect RE mechanism via dioxygen. In the absence of O2 (lower curve in the plot and lower scheme) real RE value is measured. Data from ref. 60.

Close modal

In most cases RE is measured in frozen glassy solutions, where uniform distribution of spin label orientations is present. A complete version of measurement and data analysis protocol for RE experiments on Dy(iii)–nitroxide spin pairs has been worked out in our lab over the last several years,59,61,62  and will be detailed below. The key assumptions of the data analysis procedure are as follows. For the fast relaxing Kramers type Dy(iii) centers it is assumed that only the lowest doublet plays a role in the RE. Thus, Dy(iii) is described as an effective spin S=1/2 with strongly anisotropic g-tensor (g=14, g=4.2). In the discussion section we will reconsider this approximation with respect to observed discrepancies between DEER-based and RE-based distance measurements. It is further assumed that all orientations of the g-tensor for Dy(iii) ions coupled to the detected sub-ensemble of the slowly relaxing species (nitroxide radicals) are equally probable, and that all orientations of the Dy(iii)–nitroxide inter-spin vector are also equally present in the detected ensemble of nitroxide radicals. The complete relaxation time trace V(t) can thus be presented as a weighted integral over all orientations:

formula
Equation 15

The relaxation times T1f and T2f of the fast relaxing species are not explicitly written as parameters of Δk, while the dependence of the resonance frequency on the orientation of g-tensor is explicitly indicated by the polar angle θg. While in this equation the RE decay curve for each particular orientation is mono-exponential, the overall decay V(t) is not a mono-exponential function. To characterize the RE effect from such time decay, the 1/e decay time of the RE time trace is used. It is, in principle, also possible to define the “average relaxation rate” as the slope of the orientation-averaged RE decay curve at zero time. But experimentally, due to the dead time of spectrometer, such an initial decay rate is difficult to measure precisely. Furthermore, the ‘1/e time approach’ is more stable with respect to situations, where a small fraction of orientations or species with very fast decay times are present. Such a small number of spins (or orientations) might be able to dominate in the initial decay, if they relax significantly faster than all other species, but they would not play such a significant role in determination of the 1/e decay time. It has been shown analytically and verified by numeric simulations that the average relaxation enhancement calculated from the 1/e decay time scales with an inter-spin distance r perfectly as r−6 power law.59 

The main steps in data acquisition and processing are shown in Fig. 7. First, the longitudinal relaxation data are measured with an inversion recovery experiment59–62  or, alternatively, with saturation recovery.63,89  The length of the time trace should be sufficient for the determination of the constant offset of the decay curve. This can be, for instance, measured experimentally as echo amplitude for a very long delay between the inversion pulse and the detection pulse sequence. The offset can also be fitted numerically, for instance with a multi-exponential fitting function. The set of mono-exponential decay times obtained in such fitting does not have a direct physical meaning, but the constant offset value can be determined that way precisely and reliably. The data for nitroxide–Dy(iii) pairs as well as the reference data for nitroxide radicals in the absence of Dy(iii) should be measured and corrected for the offset.

Figure 1.7

The key steps in the analysis of Ln(iii)-induced RE (see Section 3.2). (A) Longitudinal relaxation time traces measured at 80 K for nitroxide radicals in the presence of paramagnetic Dy(iii) and diamagnetic La(iii) centres. The traces are inverted and offset corrected by multiexponential fitting (see text). (B) The result of division of the two traces in (A), dotted line indicates the fit of the intermolecular RE background. (C) Intramolecular RE trace obtained from (B) after background correction (see text). Multiexponential fit to obtain the 1/e decay time is plotted as a solid line. (D) The inverted 1/e decay time from (C) is plotted as a point on the Δk(T) dependence.

Figure 1.7

The key steps in the analysis of Ln(iii)-induced RE (see Section 3.2). (A) Longitudinal relaxation time traces measured at 80 K for nitroxide radicals in the presence of paramagnetic Dy(iii) and diamagnetic La(iii) centres. The traces are inverted and offset corrected by multiexponential fitting (see text). (B) The result of division of the two traces in (A), dotted line indicates the fit of the intermolecular RE background. (C) Intramolecular RE trace obtained from (B) after background correction (see text). Multiexponential fit to obtain the 1/e decay time is plotted as a solid line. (D) The inverted 1/e decay time from (C) is plotted as a point on the Δk(T) dependence.

Close modal

In the second step, the longitudinal relaxation trace in the presence of Dy(iii) has to be divided by the reference trace, measured without Dy(iii) label, or in a sample where paramagnetic Dy(iii) is substituted by a diamagnetic La(iii) or Lu(iii). One can assume that the distances from nitroxide radicals to Dy(iii) centres and the orientations of Dy(iii) g-tensor eigenframes do not correlate with the distribution of ‘non-perturbed’ nitroxide relaxation times in the absence of Dy(iii). Under this assumption, the trace obtained by the mentioned division contains only the RE-induced contributions to the relaxation of nitroxide radicals.56,59,61,62  Due to the trace division procedure, the noise in the resulting ‘RE time trace’ (Fig. 7(B)) is growing towards long times, therefore data with good SNR are essential for proper distance extraction. On the other hand, detection in inversion recovery experiment can be done with very short inter-pulse delay, only limited by the dead time of the spectrometer, which makes the detected echo much stronger than in a DEER experiment. At X band, where RE-based distance measurements were mainly performed so far, the concentration sensitivity of RE technique seems to be somewhat better that the one of DEER.40,62 

The RE time trace contains contributions from the intramolecular Dy(iii)–nitroxide interaction as well as decay due to the interaction of nitroxide radicals with Dy(iii) centres from other molecules (intermolecular contribution). Care must be taken that the concentration of paramagnetic species in the sample is not too high so that intermolecular and intramolecular contributions can be clearly separated. Experimentally, one can see that for a concentration of labelled biomolecules of about 100 μM, the intermolecular decay is very slow and nearly linear up to the times of at least 3–4 μs.61,62 

While the RE time trace never contains oscillations, as they are observed in DEER measurements on samples with narrow distance distributions, it is still possible to automatically fit the intermolecular background with use of a general peak recognition algorithm.90  If one can assume that the background is a slowly changing smooth function that can be fitted with a polynomial of low order, then any data point with strong deviation from the background fit can be assigned to a ‘peak’ and is not fitted (assigned a constant cost function value) during the background optimization procedure, while the regions where deviations from the fitted function are below a certain threshold are being fitted with a deviation-dependent cost function.61  The intramolecular RE trace can then be obtained by dividing the full RE time trace by the background function. As long as the background is a slowly changing, almost linear function, the subtraction of the background leads to nearly the same result as division, even though mathematically this is not an exactly correct procedure.

In the case of complete labelling the intramolecular contribution decays to zero (100% effect depth) and the intermolecular contribution is mainly suppressed and to some extent incorporated into the intramolecular RE. In a more realistic case of incomplete labelling the depth of intramolecular RE effect in the RE time trace provides information on the fraction of nitroxide–Dy(iii) pairs out of all nitroxide radicals in the sample.

At the final step of data processing the intramolecular RE trace is fitted to extract the 1/e decay time. It is convenient to measure with oversampling instead of aiming at the best SNR with minimal number of data points. With that procedure the noise level is clearly seen in the processed data and further smoothing can still be performed by multi-exponential fitting of the trace. Here, as well, the individual relaxation times in such a fit would not have clear physical interpretation, but the shape of the decay trace can be fitted very precisely, thus providing a reliable estimate of the 1/e time.61,62 

An example of temperature dependence for Δk measured on Dy(iii)- and nitroxide-labelled protein molecules is shown in Fig. 7(D). The corresponding simulated values are obtained based on eqn (11)(15). Due to the very fast relaxation of Dy(iii) centres it is possible to approximate T1f(T) ≈ T2f(T)=Tf(T).

A single average Dy(iii)–nitroxide distance is assumed in such simulations.61,62  There is a certain small change in the shape of the RE trace, which is dependent on the width of Dy(iii)–nitroxide distance distribution. Studies on the possibility of extracting the width of the distance distribution from the shape of RE trace are currently still in progress in our group. To date fitting of experimental temperature-dependent Δk data thus requires adjustment of a single average inter-spin distance and of the temperature-dependent relaxation time of Dy(iii) (Tf(T)). The temperature dependence of the relaxation time can be approximated as a simple empirical power law, as the relevant range of temperatures is relatively narrow:59,61,62 

formula
Equation 16

Here, Tfopt is the optimal value of relaxation time that leads to the strongest RE. This value changes with the change of detection frequency. At X band it is approximately equal to 1.2×10−11 s. The value Tmax is the temperature at which the strongest RE is achieved. The power parameter p determines the width of the maximum in the Δk(T) dependence (Fig. 7(D)). This empirical dependence was verified experimentally by simultaneous fitting RE data at three different detection frequencies.61  Importantly, none of these three parameters influences the maximum RE value Δkmax, which is exclusively determined by the inter-spin distance.

Due to the above mentioned division approach, the length of experimentally available RE time traces is restricted by the non-perturbed longitudinal relaxation time of nitroxides T1s,0. For a perfectly mono-exponential decay one can estimate that at the time t=4T1s,0 the value V(t) for the offset corrected reference inversion recovery trace is about 2% of its initial value V(0). In the real situations the relation for the time t holds only approximately: t(2%) ≈ 4T1s,0. Division by the reference time trace at this time range will lead to an increase in SNR in the RE time trace by about a factor of 50 as compared to the SNR value at short times. While such increase can still be tolerated for very good quality measurements, this borderline case is setting the approximate limit for the accessible length of RE time trace. To estimate the decay time TΔk=1/Δk in the RE time trace it is essential to have the data at least up to t ∼ 2TΔk. This sets the limit for the ratio between the RE value Δk and non-perturbed relaxation rate k0=1/T1s,0 to be Δk/k0≥0.5. Accordingly, the detectable distance limit for the presented measurement/analysis scheme and for the Dy(iii)–nitroxide spin label pairs is approximately 4–5 nm.61,62 

Due to the connection between the non-perturbed longitudinal relaxation time of slow species and the accessible distance range, it is convenient to have the maximum on the Δk(T) curve at lowest possible temperature (T1s,0 is decreasing with temperature for nearly any type of slowly relaxing paramagnetic species in frozen glassy state). It is particularly advantageous to detect at the temperature of maximum RE, as, first, it provides access to the largest distance range (it is usually reasonably close to the optimum RE contrast temperature), and, second, at this temperature the calculated inter-spin distance is essentially insensitive to any assumptions on the particular dependence for Tf(T). Numeric simulations and frequency dependent RE measurements on orthogonally-labelled WALP23 polypeptides (S, X, and Q band) revealed that the optimum RE temperature Tmax decreases with the decrease of the measurement frequency.59,61  Unfortunately, the detection sensitivity of pulse EPR setups has the opposite tendency, showing better performance at higher detection frequencies. As a trade-off between these two tendencies, the best performance of Dy(iii)–nitroxide RE method is achieved at X-band frequencies. At Q band the optimum RE is reached at temperatures in the range 110–130 K, where nitroxide longitudinal and transverse relaxation is quite fast. As a result, the sensitivity of RE measurements at Q band is not significantly better than at X band, and the accessible distance range is worse than at X band.62  It cannot be excluded that either by changing the fast relaxing species to a species with yet shorter relaxation times than Dy(iii), or by exploiting other types of slowly relaxing species with better relaxation properties at 100–150 K, one can significantly improve the performance of the RE technique at Q band.

The RE data available so far for nitroxide radicals coupled to Dy(iii)–DOTA or Dy(iii)–DTPA labels show that the temperature of the optimum RE is rather stable for different samples. Furthermore, the RE temperature dependence is rather smooth around the maximum point. Thus the RE value of about 90% of its maximum is obtained in a range of temperatures that is at least 20 K wide, with the temperatures between 80 K and 90 K always in this range. As the actual maximum of RE is on average positioned at around 80 K, it has been suggested to use inversion recovery measurements at this single temperature for distance determination.62  This would strongly reduce the spectrometer time needed for the distance determination. On the other hand, the possible error introduced by this simplification of the method is very modest. Indeed, even assuming a 10% deviation for Δk value, the underestimation for the distance, which scales as , would be only about 2%.

As one can see from the details presented in the previous section, several assumptions have been made in order to obtain a simple and robust procedure to extract distance information. While these assumptions are intuitively clear and feasible, their verification by reference measurements with another independent method are strongly desirable to assess accuracy of the RE methodology. In the case of Fe(iii)-induced RE, which was the first target of RE studies, a detailed comparison to the distances calculated by molecular modelling has been reported.57  In the case of Dy(iii)–nitroxide pairs, direct experimental measurement of distances in homologous Gd(iii)–nitroxide pairs with DEER is possible. Fig. 8 shows the comparison between RE-based and DEER-based distance measurements. One can see that distances from RE measurements are systematically shorter than the distances measured by DEER.

Figure 1.8

Energy levels calculated for the [Dy(DOTA)] complex (ref. 93) (A) and equilibrium populations at 80 K for these energy levels (B). In (C) the correlation between Gd(iii)–nitroxide DEER data and Dy(iii)–nitroxide RE data obtained with [Dy(DOTA)] is shown (data from ref. 61 and 62). The best linear fit to the data according to the equation r(DEER)=f·r(RE) is obtained for f ≈ 1.22.

Figure 1.8

Energy levels calculated for the [Dy(DOTA)] complex (ref. 93) (A) and equilibrium populations at 80 K for these energy levels (B). In (C) the correlation between Gd(iii)–nitroxide DEER data and Dy(iii)–nitroxide RE data obtained with [Dy(DOTA)] is shown (data from ref. 61 and 62). The best linear fit to the data according to the equation r(DEER)=f·r(RE) is obtained for f ≈ 1.22.

Close modal

Independently of our group, the RE in Dy(iii)–nitroxide pairs was studied by Hirsh and coworkers on chemically modified DNA duplexes.63  Instead of the Likhtenshtein approximation91  that assumes a nearly parallel orientation of the spin of anisotropic Dy(iii) with respect to magnetic field, they considered exact formulas for strong g-anisotropy.55  The data analysis procedure was based on the same set of basic equations as discussed above, but with a significant difference in the experimental data processing and simulation: the experimental saturation recovery time traces in the presence of Dy(iii) were directly fitted to the model that, thus, included reference non-perturbed relaxation properties of nitroxide radicals as input parameters. Instead of comparing RE-based distances to reference measurements, the ratios of RE values were analysed and compared to modelled Dy(iii)–nitroxide distance ratios. Also in these studies, a measurable discrepancy between the modelled distance ratios and the corresponding RE-based values has been reported.

The data analysis approach of Hirsh et al.63  is similar to the one of S. S. Eaton, G. R. Eaton and co-workers in their studies of Fe(iii)-induced RE on iron-containing proteins.54,92  As mentioned, our data analysis procedure, described above, and the approach of Eatons and Hirsh are both based on essentially the same underlying theory and approximations. Still, in our opinion, the new procedure offers some important advantages. The most significant modification in the new procedure is the division of the relaxation trace for Dy(iii)–nitroxide pairs by the reference trace measured on isolated nitroxide radicals in the same environment.56,59,61,62  First of all, this makes it possible to remove all relaxation pathways except of the RE pathway from the analysis. Of course, this relies on the assumption of non-correlated relaxation rate distributions for different relaxation pathways, but essentially the same assumption is done indirectly in the other approach as well. Second, the RE time trace obtained after the division allows one to visually inspect and estimate the depth of the intramolecular RE effect, the steepness and curvature of the decay due to the intermolecular RE and the overall quality and sufficient length of the measured data. As the data fitting procedure is an ill-posed problem, these additional controls allow for better confidence and more precise error estimates. Finally, it is more informative to analyse the pure Δk(T) and not the complete 1/T1s(T) dependence. Such a plot can be built within each of the two approaches. On the Δk(T) diagram it is easiest to determine the maximum RE value, which is, as discussed, least sensitive to the particular model for the Tf(T) used. Nevertheless, upon careful and rigorous use, both approaches should predict nearly identical distances, especially because the RE dependence on inter-spin distance is very steep and reasonably small errors in Δk are tolerable.

As compared to the Fe(iii)–nitroxide case, where all energy levels of the lowest spin-multiplet were considered in the RE simulations, in the case of Dy(iii)–nitroxide pairs only the lowest Kramers doublet of the J=15/2 multiplet is taken into account.59,61–63  The Fig. 8 shows equilibrium populations for the 8 Kramers doublets of the lowest multiplet of Dy–DOTA complex at 80 K, according to its theoretically predicted level diagram.93  One can see that while the lowest doublet accounts for about 2/3 of the population probability, higher energy levels do contribute as well. In our work that is currently in progress we analyse the RE with taking into account all levels of the lowest Dy(iii) multiplet. The results, obtained so far, indicate that, indeed, substantial part of the discrepancy between RE and DEER might come from the truncation down to the lowest doublet. The correlation diagram shown in Fig. 8(C) also allows for an empirical correction factor f ≈ 1.2, so that rDEER=f·rRE. With this correction, distances obtained from Dy–DOTA RE measurements could be made significantly more precise.

The two discussed distance measurement approaches between non-identical spin labels bring together the strategies of nitroxide–nitroxide and Gd(iii)–Gd(iii) distance measurements, which were independent from each other before, and open possibilities for new experimental strategies. Already in the first report on Gd(iii)–nitroxide DEER on a Gd(iii) complex with a nitroxide–terpyridine derivative, the formation of mono-terpyridine complex was proved by an additional nitroxide–nitroxide distance measurement. A more detailed discussion of the idea of multiple distance measurements in a single sample was presented in the followed reports on statistically labelled ERp29 protein dimer37  and on doubly-functionalized gold nanoparticles,36  where the first example of selective distance measurements on a multiply-labelled object was given. In studies of membrane-incorporated WALP23 polypeptides (see Fig. 9), selective distance measurements were used to estimate the fraction of aggregated peptides.39,61  It has been demonstrated, in particular, that nitroxide–nitroxide distance measurements can also be performed in the presence of Dy(iii) chelates, thus combining DEER and RE in the same sample. The mobility of nitroxide labels at particular sites of WALP23 could be monitored via the EPR lineshape for La(iii)-(diamagnetic), Gd(iii)- and Dy(iii)-labelled samples, which confirms the possibility to study local properties of the nitroxide-labelled site directly on the doubly-labelled samples, without a need of additional singly-labelled ones. There is already a range of quantitative and qualitative techniques to study the local environment of nitroxide labels in biomolecules.5  As Gd(iii) labels are less spread in EPR spectroscopy, development of analogous techniques for Gd(iii) centres is still a matter of future research.

Figure 1.9

Orthogonal labelling strategy for measurements on membrane-incorporated WALP23 polypeptides. (A) Schematic representation of WALP23 in DOPC membrane, with lanthanide label at N-terminus (larger sphere outside the membrane) and nitroxide spin label at some site in the transmembrane helix (smaller sphere inside the membrane). (B) CW EPR spectra provide information on the mobility of nitroxide labels at particular labelling site. (C) Gd(iii)–nitroxide DEER provides access to the intramolecular distances. (D) Nitroxide–nitroxide DEER provides access to the relative arrangement of WALP23 molecules with respect to each other, and can be measured in the presence of Gd(iii) (see ref. 39) or Dy(iii) (see ref. 61). In the subfigures (B)–(D) the data correspond to nitroxide at site 07, 11, 15 and 19 (from bottom to top). For each nitroxide position the set of data in (B)–(D) was obtained on a single sample. Data from ref. 39.

Figure 1.9

Orthogonal labelling strategy for measurements on membrane-incorporated WALP23 polypeptides. (A) Schematic representation of WALP23 in DOPC membrane, with lanthanide label at N-terminus (larger sphere outside the membrane) and nitroxide spin label at some site in the transmembrane helix (smaller sphere inside the membrane). (B) CW EPR spectra provide information on the mobility of nitroxide labels at particular labelling site. (C) Gd(iii)–nitroxide DEER provides access to the intramolecular distances. (D) Nitroxide–nitroxide DEER provides access to the relative arrangement of WALP23 molecules with respect to each other, and can be measured in the presence of Gd(iii) (see ref. 39) or Dy(iii) (see ref. 61). In the subfigures (B)–(D) the data correspond to nitroxide at site 07, 11, 15 and 19 (from bottom to top). For each nitroxide position the set of data in (B)–(D) was obtained on a single sample. Data from ref. 39.

Close modal

Important complementary information obtained from the DEER experiment is the depth of dipolar oscillations with respect to the total echo amplitude. For different measurements performed with identical pulse settings the value of modulation depth is directly proportional to the fraction of spin pairs among all spin-labelled molecules in the sample. This information can be relevant in studies of intermolecular interactions.94,95  With use of nitroxide–nitroxide DEER the value of modulation depth is non-specific with respect to the labelling site. In contrast to this, the modulation depth in Gd(iii)–nitroxide DEER gives a more specific information on the fraction of nitroxide-labelled molecules in complex with Gd(iii)-labelled ones as compared to the total number of Gd(iii)-labelled molecules in the sample. This, in particular, allows monitoring a weak complex formation by providing an excess of nitroxide-labelled molecules, which does not prohibit Gd(iii)–nitroxide distance measurements, whereas in the nitroxide–nitroxide case a strong excess of singly-labelled molecules would reduce the modulation depth and might even make DEER measurements impossible. The opposite directionality of this effect is obtained from the Dy(iii)–nitroxide RE measurements, where the depth of intramolecular RE is proportional to the fraction of nitroxide radicals with Dy(iii) label in the same molecule out of all nitroxide radicals in the sample.61,62  Combining complementary Gd(iii)–nitroxide DEER and Dy(iii)–nitroxide RE techniques allows one to use both directionalities with very moderate additional sample preparation and labelling effort. Measurements of the DEER modulation depth and intramolecular RE effect depth made it possible to estimate the lanthanide labelling efficiency for chemo-selectively labelled T4-lysozyme as well as to prove the effect of non-specific binding of polar Ln–DOTA or Ln–DTPA tags to the surface of protein.40,62  Monitoring the Gd(iii)–nitroxide modulation depth provided direct evidence for the formation of a complex between substrate binding subunit of the vitamin B12 transporter to its transmembrane part and dependence of binding affinity on the presence or absence of non-degradable ATP-analog (see Fig. 10).95  Corresponding measurements with conventional nitroxide–nitroxide DEER were inconclusive because the transmembrane part of the transporter is a homo-dimer and labelling of both transmembrane part and substrate binding subunit led to a three labelled sites situation.

Figure 1.10

X-ray structure (PDB 2QI9) of the vitamin B12 transporter (A), and a schematic representation of its domains together with positions of spin labels (B). Measurement of Gd(iii)–nitroxide DEER allows one to monitor the stability of the complex of substrate binding domain BtuF with the transmembrane homodimeric BtuC-domain. This is observed as a change of DEER modulation depth (C) without a strong change of corresponding distance distribution (D). Data from ref. 95.

Figure 1.10

X-ray structure (PDB 2QI9) of the vitamin B12 transporter (A), and a schematic representation of its domains together with positions of spin labels (B). Measurement of Gd(iii)–nitroxide DEER allows one to monitor the stability of the complex of substrate binding domain BtuF with the transmembrane homodimeric BtuC-domain. This is observed as a change of DEER modulation depth (C) without a strong change of corresponding distance distribution (D). Data from ref. 95.

Close modal

At X band and lower frequencies Gd(iii)–Gd(iii) DEER does not perform well anymore, due to very low modulation depth. Gd(iii) labels are best suited for high-field/high-frequency distance measurements, whereas nitroxide labels exhibit stronger orientation selection and lower modulation depth under these conditions. While the lower modulation depth is a clear disadvantage in most cases, the orientation selection can be either advantageous or disadvantageous, depending on the focus of a particular study. To combine both types of labels for multiple distance measurements, the Q and W bands seem to be best suited. It is worth mentioning that at high fields the CW EPR-based distance measurements with Gd(iii) labels96  might be possible in a broader distance range than the corresponding nitroxide-based technique.97,98 

The RE distance measurements still stay somewhat aside in this scheme. It is still an open question, what precision can be achieved in RE distance measurements in multiply-labelled systems. RE measurements should also be done at X band, while all the DEER measurements in Fig. 1(A) are best performed at higher detection frequencies. Nevertheless, Dy(iii)–nitroxide RE is a useful complementary technique, easily interchangeable with Gd(iii)–nitroxide DEER, and its importance should not be underestimated.

The use of Cu(ii) or other transition metal centres as one of spectroscopically orthogonal labels for DEER measurements is complicated by the width of the corresponding EPR spectrum. A broad spectrum typically results in a strong selection of orientations and low modulation depth (if these species are pumped). While orientation selection can be useful, it clearly complicates the determination of inter-spin distance distributions. These problems might be resolved by employing pulses with very broad excitation bands, available for the pulse EPR setups based on arbitrary waveform generators. Recently such experiments were reported for Cu(ii)–nitroxide99  and Co(ii)–nitroxide spin pairs.100  It is worth mentioning recent work on DEER-based distance determination between nitroxide radicals and low-spin Fe(iii).101 

The Cu(ii) ions were also considered as possible RE agents.45,56  For the cases of Fe(iii) and Cu(ii) it is important to verify the applicability of the Redfield regime in the whole measured temperature range. The relaxation of these ions is typically slower than the one of Dy(iii) and deviations from the Redfield regime are possible at low temperatures.

An interesting future perspective of such an orthogonal labelling strategy might be a single-sample triangulation, where relative positions of several spin-labelled sites in a biomacromolecule or biomolecular complex are determined with respect to each other within a single sample, thus forming a rigid (or semi-rigid) 3D construction. Such a triangulation might be considered as a building block for structure determination of large biomolecules or their complexes. The simplest construction of this kind would be a triangular pyramid that contains six edges and four vertices, thus requiring four non-identical spin labels with a possibility to measure all pairwise distances. For the moment such label combinations are not yet offered, but measurement of all pairwise distances in a triangle Gd(iii)–nitroxide-trityl radical should be possible based on the reported performance of Gd(iii)–nitroxide35  and trityl-nitroxide47  DEER measurements.

In a biomolecule, labelled with two Gd(iii) labels and two nitroxide radicals, the measurement of Gd(iii)–nitroxide distances would in general produce an overlap of four distance distributions from all possible combinations of Gd(iii) and nitroxide labelling sites. Such measurements could provide important qualitative information, but their quantitative use might be limited. For instance the nitroxide–nitroxide and Gd(iii)–Gd(iii) distances could be monitored in two different types of biomolecules and the distance changes upon complex formation could be further supported by the independent proof of the presence of the complex from Gd(iii)–nitroxide DEER.

As EPR can only provide coarse-grained structural information and the number of distance constraints is limited by the effort to prepare multiple samples, it is interesting to see how these methods can be combined with more detailed but at the same time more short-range NMR techniques. There were already successful attempts to combine NMR and nitroxide–nitroxide DEER to obtain more detailed structural information,23,102  or to verify the consistency between EPR and paramagnetic NMR data for nitroxide radicals.103  Currently we also study in our group the performance and mutual consistency between lanthanide-induced paramagnetic relaxation enhancement or pseudo-contact shift measurements in NMR and Ln(iii)–nitroxide distance measurements in EPR.

In our view the described orthogonal labelling strategy might become popular when many EPR groups start to focus on studies of large biomolecules and, especially, their complexes. There are still clear drawbacks due to, for instance, rather low modulation depth in Gd(iii)–Gd(iii) DEER, difficulties in obtaining chemo-selectively labelled monomeric molecules or too limited choice for spectroscopically orthogonal labels. The spin dynamics of high-spin centres is also not yet fully understood and might provide interesting surprises in the future. A further progress along these lines could help establishing the new approach as one of the conventional bio-EPR tools.

The author acknowledges financial support of Swiss National Science Foundation (Grant No. 200021_121579). EPR studies on lanthanide–nitroxide pairs in our group are a joint work together with PhD students Petra Lueders (PhD 2011), Sahand Razzaghi and Luca Garbuio with continuous help and support from Prof. Gunnar Jeschke. The author had numerous fruitful discussions on the topic of this chapter with the above mentioned people and with other members of EPR group at ETH Zurich.

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